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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 16 Dec 2011 13:47:26 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/16/t1324061287h00uih1y87k24gj.htm/, Retrieved Sun, 05 May 2024 12:57:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156108, Retrieved Sun, 05 May 2024 12:57:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Survey Scores] [Intrinsic Motivat...] [2010-10-12 11:18:40] [b98453cac15ba1066b407e146608df68]
- RM D    [Central Tendency] [Paper SHW Deel 1 CT] [2011-12-16 18:47:26] [5c44e6aad476a1bab98fc6774eca4c08] [Current]
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Dataseries X:
8
5
10
8
12
6
12
9
6
5
6
10
6
8
6
7
9
10
12
11
11
11
7
11
12
6
10
7
10
10
12
11
13
7
10
12
12
12
10
10
14
14
11
12
13
11
12
12
12
9
11
14
12
15
12
11
6
12
14
12
12
14
12
14
12
11
12
10
10
12
12
11
12
12
15
12
15
11
13
14
12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156108&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156108&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156108&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.70370370370370.27857909112802738.4224948841713
Geometric Mean10.3604926941003
Harmonic Mean9.95725319270654
Quadratic Mean10.9898943478897
Winsorized Mean ( 1 / 27 )10.70370370370370.27857909112802738.4224948841713
Winsorized Mean ( 2 / 27 )10.72839506172840.27273893459522739.3357665551141
Winsorized Mean ( 3 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 4 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 5 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 6 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 7 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 8 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 9 / 27 )10.80246913580250.24306412879255844.4428768221155
Winsorized Mean ( 10 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 11 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 12 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 13 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 14 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 15 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 16 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 17 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 18 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 19 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 20 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 21 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 22 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 23 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 24 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 25 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 26 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 27 / 27 )11.11111111111110.10243938285881108.465228909328
Trimmed Mean ( 1 / 27 )10.72151898734180.27079930784337639.5921210904381
Trimmed Mean ( 2 / 27 )10.74025974025970.26170650169400141.0393309709123
Trimmed Mean ( 3 / 27 )10.74666666666670.2547518370856242.1848446300106
Trimmed Mean ( 4 / 27 )10.76712328767120.24944424371984243.164448804696
Trimmed Mean ( 5 / 27 )10.78873239436620.24314794409868144.3710615541443
Trimmed Mean ( 6 / 27 )10.81159420289860.23564983551488645.8799140651875
Trimmed Mean ( 7 / 27 )10.83582089552240.22666741319220247.8049347408143
Trimmed Mean ( 8 / 27 )10.86153846153850.21581344672420750.3283675155731
Trimmed Mean ( 9 / 27 )10.88888888888890.20253274830948653.7635961580386
Trimmed Mean ( 10 / 27 )10.90163934426230.19234662193221956.6770512252818
Trimmed Mean ( 11 / 27 )10.93220338983050.18389958441407359.4465910549058
Trimmed Mean ( 12 / 27 )10.96491228070180.1733585970853463.2498904874273
Trimmed Mean ( 13 / 27 )110.15996632642286268.7644721609855
Trimmed Mean ( 14 / 27 )11.03773584905660.15466210220024271.3667775882548
Trimmed Mean ( 15 / 27 )11.0784313725490.14777602887385774.9677160563414
Trimmed Mean ( 16 / 27 )11.12244897959180.13872798305804880.1745165929345
Trimmed Mean ( 17 / 27 )11.14893617021280.13594743571260282.0091685567507
Trimmed Mean ( 18 / 27 )11.17777777777780.13214962780950584.584254704755
Trimmed Mean ( 19 / 27 )11.20930232558140.12697232254317788.2814624562741
Trimmed Mean ( 20 / 27 )11.2195121951220.12836777918966687.4013110294982
Trimmed Mean ( 21 / 27 )11.23076923076920.1296811123728586.602968044254
Trimmed Mean ( 22 / 27 )11.24324324324320.13086341483183785.915863174525
Trimmed Mean ( 23 / 27 )11.25714285714290.13184442794927985.3820144866005
Trimmed Mean ( 24 / 27 )11.27272727272730.13252163397375785.0632982306844
Trimmed Mean ( 25 / 27 )11.29032258064520.1327423601033285.0544059323439
Trimmed Mean ( 26 / 27 )11.31034482758620.13227311903544485.507508328699
Trimmed Mean ( 27 / 27 )11.33333333333330.13074409009212386.6833317310774
Median11
Midrange10
Midmean - Weighted Average at Xnp11.3061224489796
Midmean - Weighted Average at X(n+1)p11.3061224489796
Midmean - Empirical Distribution Function11.3061224489796
Midmean - Empirical Distribution Function - Averaging11.3061224489796
Midmean - Empirical Distribution Function - Interpolation11.3061224489796
Midmean - Closest Observation11.3061224489796
Midmean - True Basic - Statistics Graphics Toolkit11.3061224489796
Midmean - MS Excel (old versions)11.3061224489796
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10.7037037037037 & 0.278579091128027 & 38.4224948841713 \tabularnewline
Geometric Mean & 10.3604926941003 &  &  \tabularnewline
Harmonic Mean & 9.95725319270654 &  &  \tabularnewline
Quadratic Mean & 10.9898943478897 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 10.7037037037037 & 0.278579091128027 & 38.4224948841713 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 10.7283950617284 & 0.272738934595227 & 39.3357665551141 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 10.6913580246914 & 0.266227633563906 & 40.1587088521559 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 10.8024691358025 & 0.243064128792558 & 44.4428768221155 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 10.679012345679 & 0.224864266667741 & 47.4909264327814 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 10.679012345679 & 0.224864266667741 & 47.4909264327814 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 10.679012345679 & 0.224864266667741 & 47.4909264327814 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 10.679012345679 & 0.174648819145619 & 61.1456315474717 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 10.679012345679 & 0.174648819145619 & 61.1456315474717 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 10.679012345679 & 0.174648819145619 & 61.1456315474717 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 10.8765432098765 & 0.138758512195107 & 78.3846917772018 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 10.8765432098765 & 0.138758512195107 & 78.3846917772018 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 10.8765432098765 & 0.138758512195107 & 78.3846917772018 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 11.1111111111111 & 0.10243938285881 & 108.465228909328 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 10.7215189873418 & 0.270799307843376 & 39.5921210904381 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 10.7402597402597 & 0.261706501694001 & 41.0393309709123 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 10.7466666666667 & 0.25475183708562 & 42.1848446300106 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 10.7671232876712 & 0.249444243719842 & 43.164448804696 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 10.7887323943662 & 0.243147944098681 & 44.3710615541443 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 10.8115942028986 & 0.235649835514886 & 45.8799140651875 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 10.8358208955224 & 0.226667413192202 & 47.8049347408143 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 10.8615384615385 & 0.215813446724207 & 50.3283675155731 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 10.8888888888889 & 0.202532748309486 & 53.7635961580386 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 10.9016393442623 & 0.192346621932219 & 56.6770512252818 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 10.9322033898305 & 0.183899584414073 & 59.4465910549058 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 10.9649122807018 & 0.17335859708534 & 63.2498904874273 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 11 & 0.159966326422862 & 68.7644721609855 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 11.0377358490566 & 0.154662102200242 & 71.3667775882548 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 11.078431372549 & 0.147776028873857 & 74.9677160563414 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 11.1224489795918 & 0.138727983058048 & 80.1745165929345 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 11.1489361702128 & 0.135947435712602 & 82.0091685567507 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 11.1777777777778 & 0.132149627809505 & 84.584254704755 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 11.2093023255814 & 0.126972322543177 & 88.2814624562741 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 11.219512195122 & 0.128367779189666 & 87.4013110294982 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 11.2307692307692 & 0.12968111237285 & 86.602968044254 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 11.2432432432432 & 0.130863414831837 & 85.915863174525 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 11.2571428571429 & 0.131844427949279 & 85.3820144866005 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 11.2727272727273 & 0.132521633973757 & 85.0632982306844 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 11.2903225806452 & 0.13274236010332 & 85.0544059323439 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 11.3103448275862 & 0.132273119035444 & 85.507508328699 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 11.3333333333333 & 0.130744090092123 & 86.6833317310774 \tabularnewline
Median & 11 &  &  \tabularnewline
Midrange & 10 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.3061224489796 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.3061224489796 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.3061224489796 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.3061224489796 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.3061224489796 &  &  \tabularnewline
Midmean - Closest Observation & 11.3061224489796 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.3061224489796 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.3061224489796 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156108&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]10.7037037037037[/C][C]0.278579091128027[/C][C]38.4224948841713[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.3604926941003[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.95725319270654[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.9898943478897[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]10.7037037037037[/C][C]0.278579091128027[/C][C]38.4224948841713[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]10.7283950617284[/C][C]0.272738934595227[/C][C]39.3357665551141[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]10.6913580246914[/C][C]0.266227633563906[/C][C]40.1587088521559[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]10.8024691358025[/C][C]0.243064128792558[/C][C]44.4428768221155[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]10.679012345679[/C][C]0.224864266667741[/C][C]47.4909264327814[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]10.679012345679[/C][C]0.224864266667741[/C][C]47.4909264327814[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]10.679012345679[/C][C]0.224864266667741[/C][C]47.4909264327814[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]10.679012345679[/C][C]0.174648819145619[/C][C]61.1456315474717[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]10.679012345679[/C][C]0.174648819145619[/C][C]61.1456315474717[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]10.679012345679[/C][C]0.174648819145619[/C][C]61.1456315474717[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]10.8765432098765[/C][C]0.138758512195107[/C][C]78.3846917772018[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]10.8765432098765[/C][C]0.138758512195107[/C][C]78.3846917772018[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]10.8765432098765[/C][C]0.138758512195107[/C][C]78.3846917772018[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]11.1111111111111[/C][C]0.10243938285881[/C][C]108.465228909328[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]10.7215189873418[/C][C]0.270799307843376[/C][C]39.5921210904381[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]10.7402597402597[/C][C]0.261706501694001[/C][C]41.0393309709123[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]10.7466666666667[/C][C]0.25475183708562[/C][C]42.1848446300106[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]10.7671232876712[/C][C]0.249444243719842[/C][C]43.164448804696[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]10.7887323943662[/C][C]0.243147944098681[/C][C]44.3710615541443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]10.8115942028986[/C][C]0.235649835514886[/C][C]45.8799140651875[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]10.8358208955224[/C][C]0.226667413192202[/C][C]47.8049347408143[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]10.8615384615385[/C][C]0.215813446724207[/C][C]50.3283675155731[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]10.8888888888889[/C][C]0.202532748309486[/C][C]53.7635961580386[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]10.9016393442623[/C][C]0.192346621932219[/C][C]56.6770512252818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]10.9322033898305[/C][C]0.183899584414073[/C][C]59.4465910549058[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]10.9649122807018[/C][C]0.17335859708534[/C][C]63.2498904874273[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]11[/C][C]0.159966326422862[/C][C]68.7644721609855[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]11.0377358490566[/C][C]0.154662102200242[/C][C]71.3667775882548[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]11.078431372549[/C][C]0.147776028873857[/C][C]74.9677160563414[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]11.1224489795918[/C][C]0.138727983058048[/C][C]80.1745165929345[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]11.1489361702128[/C][C]0.135947435712602[/C][C]82.0091685567507[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]11.1777777777778[/C][C]0.132149627809505[/C][C]84.584254704755[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]11.2093023255814[/C][C]0.126972322543177[/C][C]88.2814624562741[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]11.219512195122[/C][C]0.128367779189666[/C][C]87.4013110294982[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]11.2307692307692[/C][C]0.12968111237285[/C][C]86.602968044254[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]11.2432432432432[/C][C]0.130863414831837[/C][C]85.915863174525[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]11.2571428571429[/C][C]0.131844427949279[/C][C]85.3820144866005[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]11.2727272727273[/C][C]0.132521633973757[/C][C]85.0632982306844[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]11.2903225806452[/C][C]0.13274236010332[/C][C]85.0544059323439[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]11.3103448275862[/C][C]0.132273119035444[/C][C]85.507508328699[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]11.3333333333333[/C][C]0.130744090092123[/C][C]86.6833317310774[/C][/ROW]
[ROW][C]Median[/C][C]11[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.3061224489796[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156108&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156108&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10.70370370370370.27857909112802738.4224948841713
Geometric Mean10.3604926941003
Harmonic Mean9.95725319270654
Quadratic Mean10.9898943478897
Winsorized Mean ( 1 / 27 )10.70370370370370.27857909112802738.4224948841713
Winsorized Mean ( 2 / 27 )10.72839506172840.27273893459522739.3357665551141
Winsorized Mean ( 3 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 4 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 5 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 6 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 7 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 8 / 27 )10.69135802469140.26622763356390640.1587088521559
Winsorized Mean ( 9 / 27 )10.80246913580250.24306412879255844.4428768221155
Winsorized Mean ( 10 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 11 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 12 / 27 )10.6790123456790.22486426666774147.4909264327814
Winsorized Mean ( 13 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 14 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 15 / 27 )10.6790123456790.17464881914561961.1456315474717
Winsorized Mean ( 16 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 17 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 18 / 27 )10.87654320987650.13875851219510778.3846917772018
Winsorized Mean ( 19 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 20 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 21 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 22 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 23 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 24 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 25 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 26 / 27 )11.11111111111110.10243938285881108.465228909328
Winsorized Mean ( 27 / 27 )11.11111111111110.10243938285881108.465228909328
Trimmed Mean ( 1 / 27 )10.72151898734180.27079930784337639.5921210904381
Trimmed Mean ( 2 / 27 )10.74025974025970.26170650169400141.0393309709123
Trimmed Mean ( 3 / 27 )10.74666666666670.2547518370856242.1848446300106
Trimmed Mean ( 4 / 27 )10.76712328767120.24944424371984243.164448804696
Trimmed Mean ( 5 / 27 )10.78873239436620.24314794409868144.3710615541443
Trimmed Mean ( 6 / 27 )10.81159420289860.23564983551488645.8799140651875
Trimmed Mean ( 7 / 27 )10.83582089552240.22666741319220247.8049347408143
Trimmed Mean ( 8 / 27 )10.86153846153850.21581344672420750.3283675155731
Trimmed Mean ( 9 / 27 )10.88888888888890.20253274830948653.7635961580386
Trimmed Mean ( 10 / 27 )10.90163934426230.19234662193221956.6770512252818
Trimmed Mean ( 11 / 27 )10.93220338983050.18389958441407359.4465910549058
Trimmed Mean ( 12 / 27 )10.96491228070180.1733585970853463.2498904874273
Trimmed Mean ( 13 / 27 )110.15996632642286268.7644721609855
Trimmed Mean ( 14 / 27 )11.03773584905660.15466210220024271.3667775882548
Trimmed Mean ( 15 / 27 )11.0784313725490.14777602887385774.9677160563414
Trimmed Mean ( 16 / 27 )11.12244897959180.13872798305804880.1745165929345
Trimmed Mean ( 17 / 27 )11.14893617021280.13594743571260282.0091685567507
Trimmed Mean ( 18 / 27 )11.17777777777780.13214962780950584.584254704755
Trimmed Mean ( 19 / 27 )11.20930232558140.12697232254317788.2814624562741
Trimmed Mean ( 20 / 27 )11.2195121951220.12836777918966687.4013110294982
Trimmed Mean ( 21 / 27 )11.23076923076920.1296811123728586.602968044254
Trimmed Mean ( 22 / 27 )11.24324324324320.13086341483183785.915863174525
Trimmed Mean ( 23 / 27 )11.25714285714290.13184442794927985.3820144866005
Trimmed Mean ( 24 / 27 )11.27272727272730.13252163397375785.0632982306844
Trimmed Mean ( 25 / 27 )11.29032258064520.1327423601033285.0544059323439
Trimmed Mean ( 26 / 27 )11.31034482758620.13227311903544485.507508328699
Trimmed Mean ( 27 / 27 )11.33333333333330.13074409009212386.6833317310774
Median11
Midrange10
Midmean - Weighted Average at Xnp11.3061224489796
Midmean - Weighted Average at X(n+1)p11.3061224489796
Midmean - Empirical Distribution Function11.3061224489796
Midmean - Empirical Distribution Function - Averaging11.3061224489796
Midmean - Empirical Distribution Function - Interpolation11.3061224489796
Midmean - Closest Observation11.3061224489796
Midmean - True Basic - Statistics Graphics Toolkit11.3061224489796
Midmean - MS Excel (old versions)11.3061224489796
Number of observations81



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')